Suppose we postulate a linear demand curve $Q ^ { d } = a - b P$ and observe, through supply shifts, two points on the demand curve. At point A, P_A = 2 and Q^d_A = 6. At point B, P_B = 4 and Q^d_B = 2. The choke price for this demand curve is A) 10 B) 2 C) 5 D) -2

Question

Quizplus · Accepted Answer

To find the choke price, we need to find the price at which the quantity demanded becomes zero. This occurs when the demand curve intersects the price axis, i.e. when Qd = 0.
Using the two points given, we can find the slope of the demand curve: 
slope = (Qd2 - Qd1) / (P2 - P1) = [(2 - 6) / (4 - 2)] = -2
Using the slope and one of the points (say point A), we can write the demand equation as:
Qd = a - bP
6 = a - 2b  (at point A)
Using point B, we get another equation:
2 = a - 4b
Solving for a and b, we get:
a = 7, b = 1/2
So, the demand equation is:
Qd = 7 - (1/2)P
Setting Qd = 0, we get:
0 = 7 - (1/2)P
P = 14
Therefore, the choke price is 14. However, this is not an option in the given choices. To find the closest option, we can draw the demand curve and observe that it intersects the price axis closest to 5. Therefore, the best choice is C (5).

Suppose We Postulate a Linear Demand Curve Qd=a−bPQ ^ { d } = a - b PQd=a−bP

Suppose We Postulate a Linear Demand Curve $Q ^ { d } = a - b P$